1.3 Basic Commands

In this section, you will learn how to enter mathematical expressions, functions, points, equations, inequalities, and commands in the GeoGebra Graphing Calculator.

The Graphing Calculator contains an Algebra View, where you enter mathematical information, and a Graphics View, where graphs and objects are displayed. Each entry you create in the Algebra View is connected to its representation in the Graphics View.

By the end of this section, you will be able to:

Enter calculations and mathematical expressions
Use fractions, exponents, roots, and constants
Create and name variables
Graph and name functions
Create points using coordinates
Graph equations and inequalities
Create sliders
Use commands to locate roots, extrema, and intersections
Edit, hide, and delete objects

Basic GeoGebra Commands.mp4

Step 1: Open the Graphing Calculator

Go to the GeoGebra website.
Open the Graphing Calculator.
Locate the Algebra View on the left side of the screen.
Locate the Graphics View on the right side of the screen.
Select the input field in the Algebra View.

The Algebra View displays the mathematical definitions of your objects and allows you to enter expressions and commands. The Graphics View displays their visual representations.

Step 2: Enter a Basic Calculation

Begin by using GeoGebra as a calculator.

Select the input field.
Type: 3 + 5

Press Enter.
GeoGebra will display the result: 8

Try entering the following calculations one at a time:

12 - 7
4 * 6
20 / 5

Press Enter after each entry.

GeoGebra automatically labels calculations entered into the Algebra View. You can also assign your own labels later in this tutorial.

Step 3: Enter Fractions, Exponents, and Roots

GeoGebra uses symbols and typed commands to represent common mathematical operations.

Fractions

Use a forward slash / to enter a fraction.

Type:

1 / 4

Exponents

Use the caret symbol ^ to enter an exponent.

Type:

2^3

Then try:

x^2

Square Roots

Use the sqrt command and place the expression inside parentheses.

Type:

sqrt(25)

Then try:

sqrt(x)

GeoGebra supports typed notation such as / for fractions, ^ for exponents, and sqrt(x) for square roots.

Step 4: Use Parentheses Correctly

Parentheses tell GeoGebra which operations should be completed together.

Compare these entries:

2^3 / 4

2^(3 / 4)

Now compare:

sqrt(4^2) + 9

sqrt(4^2 + 9)

Use parentheses whenever you need to clearly identify the numerator, exponent, input, or grouped expression.

Step 5: Use Mathematical Constants

GeoGebra recognizes commonly used mathematical constants.

Type:

You can use pi inside other expressions:

2 * pi

sin(pi / 2)

GeoGebra also recognizes e as Euler’s number.

Step 6: Create and Name a Variable

You can assign a number to a variable by typing the variable name, an equal sign, and its value.

Type:

a = 2

Then type:

b = -3

You can now use these variables in other expressions.

For example, type:

a + b

GeoGebra will use the current values of a and b to calculate the result.

Assigning names to values allows you to reuse them in functions and other commands. GeoGebra uses lowercase letters for numbers and variables unless you specify another valid name.

Step 7: Graph and Name a Function

A function can be entered using standard function notation.

Type:

f(x) = 2x + 1

Press Enter.

GeoGebra will:

Display the function in the Algebra View
Draw its graph in the Graphics View
Assign the name fff to the function

Now enter:

g(x) = x^2 - 4

Try several additional functions:

h(x) = x^3

p(x) = abs(x)

q(x) = sqrt(x)

GeoGebra supports standard function notation as well as common functions such as absolute value, square root, sine, cosine, tangent, logarithms, floor, and ceiling.

Step 8: Use Multiplication Correctly

GeoGebra understands several forms of multiplication.

These entries are interpreted as multiplication:

2 * x

When using named variables, it is usually clearer to include the multiplication symbol.

For example, enter:

a = 2

Then enter:

f(x) = a * x^2

Using * helps GeoGebra distinguish multiplication from a longer variable name.

Tip: When creating materials for other users, use explicit multiplication symbols and parentheses to make commands easier to read and troubleshoot.

Step 9: Create a Point

Points are entered as ordered pairs inside parentheses.

Type:

A = (2, 3)

Press Enter.

GeoGebra will create point AAA at (2,3)(2,3)(2,3).

Now enter:

B = (-1, 4)

Points are typically named using capital letters. GeoGebra will automatically use capital letters when it labels unnamed points.

After creating a point:

Locate it in the Graphics View.
Select and drag the point.
Observe how its coordinates change in the Algebra View.

Step 10: Enter an Equation

GeoGebra can graph equations directly.

Enter:

y = 2x + 3

Then try:

x = 4

The first equation creates a slanted line. The second creates a vertical line.

You can also enter an equation that is not written as a function of xxx.

Type:

x^2 + y^2 = 25

GeoGebra will graph a circle centered at the origin with a radius of 5.

The Graphing Calculator is designed to visualize and analyze functions, equations, and inequalities in two dimensions.

Step 11: Enter an Inequality

GeoGebra can graph and shade the solution region of an inequality.

Enter:

y > 2x + 1

Observe the boundary line and shaded region.

Now try:

y <= x^2

You can type the following symbols when entering inequalities:

Compare:

y > 2x + 1

and

y >= 2x + 1

Observe the difference between the boundary lines. A strict inequality uses a boundary that is not included, while an inclusive inequality includes the boundary.

Step 12: Create a Slider

A slider allows you to change the value of a variable dynamically.

Enter:

a = 1

Open the menu for the variable aaa.
Select Create Slider if a slider is not already displayed.
Adjust the value of aaa.

Now enter:

f(x) = a * x^2

Move the slider and observe how the graph changes.

Create two more variables:

h = 0

k = 0

Then replace the function with:

f(x) = a * (x - h)^2 + k

Adjust the sliders for a, h, and k. Because the function depends on these variables, the graph updates whenever a slider value changes. Sliders are supported in the Graphing Calculator and can be created from numerical variables.

Step 13: Find the Roots of a Function

GeoGebra commands perform specific mathematical actions.

First, create the function:

f(x) = x^2 - 4

Then enter:

Roots(f)

GeoGebra will identify the points where the graph crosses the xxx-axis.

When you begin typing a command, GeoGebra provides automatic command suggestions and syntax guidance.

Step 14: Find an Extremum

Use the Extremum command to locate a maximum or minimum point.

With the function

f(x) = x^2 - 4

already entered, type:

Extremum(f)

GeoGebra will identify the minimum point of the parabola.

The point will appear in both the Algebra View and Graphics View.

Step 15: Find the Intersection of Two Functions

Create two functions:

f(x) = x^2 - 4

g(x) = x

Then enter:

Intersect(f, g)

GeoGebra will create points at the locations where the two graphs intersect.

Commands generally use the following structure:

CommandName(object, object)

The objects inside the parentheses tell GeoGebra what the command should use.

Step 16: Edit an Existing Entry

To change an object you already created:

Select the expression in the Algebra View.
Click or press Enter to edit it.
Change the expression.
Press Enter to confirm the change.

For example, change:

f(x) = x^2 - 4

to:

f(x) = x^2 - 9

The graph and all objects that depend on fff will update automatically.

Step 17: Hide or Show an Object

Each entry in the Algebra View has a visibility control.

Locate an expression in the Algebra View.
Select the visibility icon next to it.
Observe that the object disappears from the Graphics View.
Select the icon again to display the object.

Hiding an object does not delete it. The object remains part of the construction.

Step 18: Delete and Undo

To delete an object:

Select the object or expression.
Open its menu.
Select Delete.

You can also press the Delete or Backspace key after selecting an object.

To reverse your most recent action, use:

Ctrl + Z on Windows
Command + Z on a Mac

GeoGebra also supports redo when undo and redo are enabled in the application.

Basic Commands Practice

Open a blank Graphing Calculator and enter each of the following items in order:

3 + 5

1 / 4

2^3

sqrt(25)

a = 2

f(x) = a * x^2

A = (2, 3)

g(x) = x^2 - 4

y > x - 2

Roots(g)

Extremum(g)

h(x) = x

Intersect(g, h)

After entering the commands:

Create a slider for aaa.
Move the slider and observe the graph of fff.
Move point AAA.
Hide one function.
Edit one function.
Delete one object.
Use Undo to restore the deleted object.

Check Your Understanding

Before moving to the next section, make sure you can:

Enter a calculation in the Algebra View
Use /, ^, and sqrt
Use parentheses to group expressions
Create and name a variable
Create and name a function
Enter a point as an ordered pair
Graph an equation
Graph an inequality
Create and adjust a slider
Find roots, extrema, and intersections
Edit, hide, and delete an object

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